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Upper and Lower Bounds for the Kagomé Lattice Bond Percolation Critical Probability

Published online by Cambridge University Press:  28 January 2003

JOHN C. WIERMAN
JOHN C. WIERMAN
Affiliation:
Mathematical Sciences Department, 104 Whitehead Hall, Johns Hopkins University, Baltimore, Maryland, MD 21218-2682, USA (e-mail: wierman@jhu.edu)
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Abstract

The bond percolation critical probability of the Kagomé lattice is greater than 0.5209 and less than 0.5291. The proof of these bounds uses the substitution method, comparing the percolative behaviour of the Kagomé lattice bond model with that of the exactly solved hexagonal lattice bond model via stochastic ordering.

Type
Research Article
Information
Combinatorics, Probability and Computing , Volume 12 , Issue 1 , January 2003 , pp. 95 - 111
Copyright
2003 Cambridge University Press

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